Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo.

Area of Science:

• Materials Science
• Computational Physics
• Analytical Chemistry

Background:

• Bayesian inference methods, particularly random-walk Markov Chain Monte Carlo (MCMC), are increasingly used for X-ray scattering analysis.
• Hamiltonian MCMC represents a significant advancement in MCMC, utilizing Hamiltonian dynamics for more efficient parameter sampling.

Purpose of the Study:

• To elucidate the principles of Hamiltonian MCMC for inversion problems in X-ray scattering.
• To demonstrate its application in estimating high-dimensional models across various X-ray scattering techniques.

Main Methods:

• Application of Hamiltonian MCMC to X-ray scattering inversion problems.
• Estimation of high-dimensional models in small-angle X-ray scattering (SAXS).
• Utilizing Hamiltonian MCMC for reflectivity and X-ray fluorescence holography analyses.

Main Results:

• Hamiltonian MCMC demonstrates superior performance compared to random-walk MCMC with effective preconditioning.
• Efficiently handles complex, high-dimensional models common in X-ray scattering.
• Provides robust statistical analysis of parameter distributions.

Conclusions:

• Hamiltonian MCMC is an efficient and powerful tool for X-ray scattering data analysis.
• It enables accurate statistical analysis, model prediction, and confidence assessment.
• This method enhances the capabilities of Bayesian inference in materials characterization.